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g A small ball is tied to one end of a light 2.5-m wire, and the other end of the wire is hooked to the ceiling. A person pulls the ball to the side until the wire makes an angle of 35° with the plane of the ceiling and then gently releases it. What is the angular speed of the ball, in rad/s, as it swings through its lowest point?

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Onyebuchinnajiidn

The angular speed of the ball as it swings through its lowest point is 1.8 rad/s.

The given parameters;

radius of the circular path, r = 2.5 m

angle with the vertical, θ = 35⁰

The angular speed of the ball, as it swings through its lowest point is calculated as follows;

[tex]Tcos \theta = m\omega ^2 r\\\\mgcos \theta = m \omega ^2 r\\\\gcos \theta = \omega ^2 r\\\\\omega ^2 = \frac{gcos \theta }{r} \\\\\omega = \sqrt{\frac{gcos \theta }{r} } \\\\\omega = \sqrt{\frac{9.8 \times cos (35) }{2.5} } \\\\\omega = 1.8 \ rad/s[/tex]

Thus, the angular speed of the ball as it swings through its lowest point is 1.8 rad/s.

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